Student Worksheet for Uniform Circular Motion

1 Advanced PhysicsUniform Circular Motion Student Worksheet for Uniform Circular Motion After you ve worked through the sample problems in the videos, you can work out the problems below to practice doing this yourself. Answers are given on the last page. Friction: Fk = kN Fs = sN Centripetal Force: a F=m=Rmv2 Law of Gravitation: F=r2Gm m12 Free-fall acceleration: go=r2GM Gravitational Potential Energy: )U= (r122Gm m12+r132Gm m13+r232Gm m23+.. Escape Speed: v= R2GM Law of Periods: ) r3T2=(4 2GM Energy in Planetary Motion : E = K + U and K U= rGMm=2rGMm 2014 Supercharged 1 Advanced PhysicsUniform Circular Motion Practice Problems: car travels around a corner on an unbanked track.

2 The radius of the track is 12 meters and the car is traveling at a velocity of 5 meters per second. Find the angle that a strap hanging from the inside of the car will make as the car travels around the corner. Student stands on a merry-go-round of radius m. The merry-go-round revolves once every 30 seconds. Find the speed of the child on the outer rim of the merry-go-round. What must be the coefficient of static friction between the boys shoes and the merry-go-round for him to stay on the merry-go-round? bicyclist rides in a circle with a radius of 20 m at a speed of 5 m/s.

3 If the combined mass of the bike and the rider is 90 kg, what is the force of friction exerted on the bike by the road? What is the total force exerted by the road on the bike? 2014 Supercharged 2 Advanced PhysicsUniform Circular Motion child of mass 73 kg is on a Ferris wheel. At the top of the Ferris wheel the child has an apparent weight of 637N. What is the child s apparent weight at the lowest point? Find the apparent weight of the Student at the highest point if the speed of the Ferris wheel was tripled. car driver takes a turn of radius 10 m at a speed of 25 m/s.

4 How many g s of acceleration will the the driver experience? 11kN car rounds an unbanked curve with a radius of 70 m at a speed of 15 m/s. Find the force of friction of the road on the tires to keep the car on its path. If the coefficient of friction between the tires and the road is , will the car slip out of its turn? 2014 Supercharged 3 Advanced PhysicsUniform Circular Motion takes more energy: Putting a satellite up to 1500 km or putting a satellite in orbit that is already at 1500 km? What about at 3000 km and 4500 km instead of 1500km? The Earth s radius is 6000 km.

5 8. An asteroid with mass times the mass of the Earth revolves in a Circular orbit around the sun. The asteroid s orbit is times that of Earth s. Find the period the asteroid s revolution in Earth years. What is the ratio between the kinetic energy of the asteroid and Earth? the Earth travels in a Circular orbit, how far does the Earth travel in 70 seconds? 2014 Supercharged 4 Advanced PhysicsUniform Circular Motion 10. Phobos orbits the planet Mars at a radius of m with a period of 8 hours. Find the mass of Mars. 11. If a satellite is placed into orbit, around the Earth, at a radius of three quarters of the Moon s orbit radius, what is the satellite s period of revolution in lunar months?

6 12. A spaceship is 77,850 light years from the center of a galaxy. The mass of the galaxy times the mass of our sun. Assume the galaxy acts as a spherical distribution so you can use of the law of gravitation. What minimum speed must the spaceship have to escape the galaxy? 2014 Supercharged 5 Advanced PhysicsUniform Circular Motion 13. What is the escape velocity of a planet of radius 700 km with gravitational acceleration one half of Earth s gravitational acceleration? How high will a particle go if it is launched up with an initial speed of 998 m/s on this planet ?

7 What speed will the object reach if it is dropped from a height of 2000 km (2300 km from the center of the planet ?) 14. In a double star system, two stars orbit about their shared center of mass. Both stars share the same mass of kg and are a distance of m from each other. What is their angular speed? If a meteorite travels through the center of mass between the two planets what must its speed be to escape the gravitational field of the two stars? 15. Find the gravity on the surface of the moon. What is the period of a pendulum on the moon, if the pendulum normally has a period of three seconds on Earth?

8 2014 Supercharged 6 Advanced PhysicsUniform Circular Motion 16. A person weighs 600 N at sea level on Earth. If you ride an elevator up to 500 meters, what will be your new apparent weight? 17. If you draw a line from the center of Earth to the center of the Sun. Where must a particle be on that line in order for the gravitational field of the Earth and the Sun the cancel eachother out? 18. What is the ratio between Earth s acceleration towards the sun when the moon is between the Earth and the sun compared to when the Earth is between the moon and the sun?

9 2014 Supercharged 7 Advanced Physics Uniform Circular Motion 2014 Supercharged Science Page 1 Student Worksheet for Uniform Circular Motion After you ve worked through the sample problems in the videos, you can work out the problems below to practice doing this yourself. Answers are given on the last page. Friction: Fk = kN Fs = sN Centripetal Force: F = ma = mRv2 Law of Gravitation: F = Gmr12m2 Free-fall acceleration: go = GrM2 Gravitational Potential Energy: U = (Gmr112m2 2 + Gmr113m2 3 + Gmr223m2 3 + ..) Escape Speed: v = 2 GRM Law of Periods: Tr32 = (G4 M2) Energy in Planetary Motion : E = K + U U = GMr m and K = G2 Mrm Adva 20 Prac 1 2 anced Physic014 Superchctice Problem1.

10 A car travis traveliof the car2. A studenseconds. coefficienmerry gocs harged Scienms: vels aroundng at a velocr will make ant stands on Find the spent of static fro round? Unifnce corner oncity of 5 metas the car tra merry go eed of the chriction betw form CirculacienceLearnin an unbanketers per secoavels aroun round of radhild on the oween the boyar Motion track. Theond. Find thed the cornerdius m. Touter rim of tys shoes andme radius of te angle that r. The merry gthe merry gd the merry gthe track is 1a strap hanggo round revgo round. Whgo round for12 meters anging from thvolves once hat must ber him to stayPage 2nd the car he inside every 30 the y on the 2 Adva 203 4 anced Physic014 Superch3.